BAGHDAD — Al-Qaida’s branch in Iraq has claimed responsibility Tuesday for a wave of bombings across the country that killed at least 58 people, most of them in predominantly Shiite Muslim areas.

The Islamic State of Iraq and the Levant, the al-Qaida affiliate in Iraq, took credit for the attacks on a website commonly used by Sunni extremists. The authenticity of the statement could not be independently verified, but its style was consistent with earlier al-Qaida statements.

The blasts on Monday — 18 in all — were the latest in a surge of bloodshed that has swept across Iraq since April, killing more than 3,000 people and worsening the already strained ties between Iraq’s Sunni minority and the Shiite-led government. In July alone, nearly 700 people have been killed in insurgent attacks, according to an Associated Press count.

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The scale and pace of the violence have fanned fears of a return to the widespread sectarian bloodletting that pushed Iraq to the brink of civil war after the 2003 U.S.-led invasion.

Al-Qaida’s Iraqi branch and other Sunni insurgent groups have targeted the country’s security forces in a bid to undermine faith in the Shiite-led government and to stir up sectarian tensions. But the group has grown emboldened in recent months following a government crackdown on Sunni protests calling for better treatment by the state.

Last week, the group carried out simultaneous attacks on two prisons that allowed hundreds of inmates, including senior al-Qaida members, to escape and left dozens of people dead.

A spokesman for al-Qaida in Iraq, Abu Mohammed al-Adnani, described the jailbreak as a “great victory” in an audio message posted on the same website Tuesday.

Last year, al-Qaida launched a campaign called “Breaking the Walls” that made freeing its imprisoned members a top priority. Al-Adnani said that effort came to a close with the twin attacks on the prison, and announced a new campaign dubbed “The Harvest of the Soldiers.” He did not specify what the new operation aims to achieve.

Violence continued on Tuesday. In the afternoon, a bomb missed a police patrol in Tarmiyah, killing two civilian passers-by and wounding seven others, officials said. Tarmiyah is 50 kilometers (30 miles) north of Baghdad.

Gunmen also killed three policemen in two separate shootings in the northern city of Mosul, authorities said.

Hospital officials confirmed the death tolls in the attacks. All officials spoke on condition of anonymity because they are not authorized to release information to the media.